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1) A bag contains 4 gold marbles, 6 silver marbles, and 32 black marbles. Someone offers to play
this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver,
you win $2. If it is black, you lose $1. What is your expected value if you play this game?
the expected value of playing this game = a weighted average of the winnings (or losses) multiplied by the odds of winning: (3/37)3 + (9/37)2 + (25/37054)(-1) = 9/37 + 18/37 - 25/37 = 27/37 -25/37 = 2/37 = about 0.054 winnings = $0.054 = 5.4 cents
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